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1:Rh5+ Nxh5
2:Qxh5 Kg8
3:Bc4+ Kf8
4:Qh8+
There is no way to have a draw: Neither fortress (…axb1Q is looming), nor stalemate (too many mobile pawns), nor repetition or perpetual chess (black rooks and knight will take all that is near the king after the second check)
Black queen has no more mobility, but cannot be trapped in order to reduce the material imbalance (because axb1Q with check again)
So, White can’t save the game.
He can only win.
1.Rh5+!! does the trick
1…Nxh5
2.Qxh5+ Kg8
3.Bc4+ Rf8
4.Qh8#
1…Kg8
2.Bc4+ Kf8
3.Rh8+ Ng8
4.Rxg8#
Black of course may interpose all the pieces he want but with no avail.
1.Rh5+ Nxh5 2.Qxh5+ Kg8 3.Bc4+ Qe6 4.Bxe6+ Rf7 5.Qxf7+ Kh7 6.Qh5#
1. Rh5+ Nxh5 (…Kg8 2. Bc4+)
2. Qxh5+ Kg8
3. Bc4+ Kf8
4. Qh8#
Pretty simple since Rh5 is about the only viable check:
1. Rh5 Nh5 (Kg8 2.Bc4)
2. Qh5 Kg8
3. Bc4 Qe6 (just delay; Kf8 4.Qh8#)
4. Be6 Rf7
5. Qf7 Kh8/7
6. Qh5#
Rh5+
1. Rh5+ Nxh5
2. Qxh5+ Kg8
3. Bc4+ Kf8
4. Qh8#
White Wins!